"Ben Goertzel" <ben@goertzel.org> writes:
> As a Peircean pragmatist, my question is: What measurement could I make,
> whose result would come out differently if these other universe existed,
> versus if they did not exist?

Well, for Level I, that's easy. You measure the curvature of space
using an experiment like the WMAP cosmic background radiation
measurement. We assume that a non-flat curvature would mean
"finite". Of course, flat does not mean "infinite", but the hypothesis
certainly has falsifiable consequences like the curvature measurement.

For Level II, it seems to be argued that there are consequences around
us that lead to observables that falsify or don't falsify the
hypothesis -- apparently the very uniformness of matter in the
universe seems to lend credence to the "perpetual chaotic inflation"
notion, and there are reputedly other observables, though I'm not sure
what they are really given how poorly I understand the physics. In any
case, though, there are again falsifiable consequences.

For Level III, I'm not sure what the experiments one might conduct
are, but of course the ones we have conducted so far are indeed
consistent with the hypothesis. The problem is that they are also
apparently consistent with other hypotheses, too.

For Level IV, you should read Tegmark's paper. He makes some
reasonable claims about ways you can test consequences of the theory
-- although I tend to dispute some of his claims about the paucity of
structures that might support self aware systems, which makes some of
his proposed tests a bit more difficult.